Let us finally mention that one may also consider the scheme–invariant singlet
evolution [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]}, [11]}
in addition to the one in the flavor non–singlet case, provided the corresponding flavor decomposition can be
carried out. This will usually require more than just the deep–inelastic data, because of the sea–quark
combinations. A possible way would consist in referring to the Drell–Yan cross section here. Already this part
complicates the
analysis. Furthermore, one needs to measure the slope \(\partial F_i/\partial \ln (Q^2)\)  at the input scale \(Q_0^2\) 
together with \(F_i(Q_0^2)\)  in an uncorrelated way. A second possibility would consist in using the pair \(F_2^{\rm S}(Q_0^2),F_L^{\rm S}(Q_0^2)\) . However, the measurement of the structure function \(F_L^{\rm S}\)  is much more difficult than
that of \(F_2^{\rm S}\)  and in the past not enough statistics has been collected in this case,
cf. [12]}, [13]}, [14]}, see, however, [15]}.
To perform the necessary flavor decomposition, one needs to perform all these measurements both at proton and
deuteron targets.
By scheme–invariant evolution the fitting problem of input distributions does not exist and no further optimization by
neural network techniques is necessary since the input distribution is fully determined by its
measurement.
